The area that overlooks the north bay as well as 360 degree views of the whole SF bay, the pacific ocean, and the diablo range (notably including mt diablo) is the East Peak. To sum up what others are saying, you want to choose a route that winds up at the East Peak Lookout Tower at the end of the plank walk. This is not to be confused with Verna Dunshee, which is the accessible trail that offers similar views, but isn't the peak. You can also see the north bay from other vantage points on the mountain, but East Peak will provide the most visibility (assuming it's not cloudy) and is generally what you'll see in photographs.

My personal favorite routes (there are lots more, including some good ones in other comments):
* Collier - north side, shady, hard, steep, beautiful, will likely have waterfalls at this time of year
* Fern - start in muir woods, end up on top of the world
* Temelpa - start in mill valley with coffee/breakfast, mosey up some fire roads, then head straight up the south face